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C₂²×#2740 #7633533

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

8294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

(1,2);(3,4);(5,6)(7,9)(8,10)(11,12)(13,14,16,18)(15,19,20,17)(22,25)(26,27);(6,7)(8,12)(13,14,16,18)(15,17,20,19)(21,22,24,25)(23,27,28,26);(5,7,9,6)(8,11,12,10)(13,14)(15,17)(16,18)(19,20)(21,23,24,28)(22,26,25,27);(5,8)(6,10)(7,11)(9,12)(13,15)(14,17)(16,20)(18,19)(21,22)(23,26)(24,25)(27,28)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540729);